Contextuality-enhanced quantum state discrimination under fixed failure probability

Abstract

Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit contextuality-enhanced success probabilities that surpass classical bounds, offering significant advantages for quantum sensing and communication. However, in practice, both error and failure outcomes can occur, suggesting the need for a unified strategy that incorporates both aspects while exploring the potential for contextuality enhancement. In this work, we theoretically demonstrate contextuality enhancement in quantum state discrimination under a fixed failure probability. We show that this enhancement disappears within a certain intermediate range of failure probabilities--a phenomenon absent in conventional strategies, where both minimum-error and unambiguous discrimination consistently outperform the noncontextual bound for equal priors. Moreover, we analyze how the existence of this non-enhancement region depends on the confusability of the quantum states, which corresponds to their fidelity in a quantum model. We further extend the discussion to the noisy state discrimination, which even encompasses the maximal-confidence discrimination. In this extended discussion, we observe that the non-enhancement region tends to disappear with increasing noise strength.

Figures (4)

• Figure 1: (a) Strategy for discriminating one of two quantum states $|\psi_1\rangle$ and $|\psi_2\rangle$, prepared with prior probabilities $q_1$ and $q_2$, respectively. Here, a measurement for discriminating these quantum states is established to output one of three outcomes $y=0,1,2$. If $y=1,2$, then one can identify the prepared state as $|\psi_y\rangle$, although incorrect sometimes. Otherwise, i.e., $y=0$, it means that the identification is failed. In the strategy, the probability $p(0|x)$ is fixed to a constant $Q_x$, leading to the fixed failure probability $Q=q_1Q_1+q_2Q_2$. (b) Representation of measurement probability. In a quantum model, conditional probability to obtain $y$ for given $|\psi_x\rangle$ is represented by $p(y|x)=\langle\psi_x|\hat{M}_y|\psi_x\rangle$. Meanwhile, in a noncontextual model, this conditional probability represented in terms of a hidden variable $\lambda$, based on the Bayesian theorem.
• Figure 2: (a) Contextuality-enhanced success probability investigated across $0.5\le q_1\le 0.6$ for the better visibility, given confusability 0.6. Here, the surface colored in rainbow is the maximum success probability under the quantum model, and the gray surface is the noncontextual bound. The shaded area on the 2d plot consisting of $Q$ and $q_1$ axes shows the region where there is non-enhancement. (b) The specified contextuality enhancement in the case of equal priors. Here, the red (gray) lines show the maximum success probability of the quantum model (the noncontextual bound). The region with non-enhancement is observed to $0.245\le Q\le0.7736$.
• Figure 3: Contextuality-enhanced success probability investigated across $0.5\le q_1\le 0.6$ for the better visibility. Here, the surface colored in rainbow is the maximum success probability under the quantum model, and the gray surface is the noncontextual bound. The shaded area on the 2d plot consisting of $Q$ and $q_1$ axes shows the region where there is non-enhancement. Here, the confusabilities are assumed to be $0.4$, $0.6$, and $0.8$ in (a), (b), and (c), respectively.
• Figure 4: Contextuality-enhanced success probability investigated across $0\le Q,\epsilon\le 1$ for given confusability $c_{\psi_1,\psi_2}=0.4$. Here, the surface colored in rainbow is the maximum success probability under the quantum model, and the orange surface is the noncontextual bound.